Given that two data sets have the same median, range, and interquartile range, we are asked if the box-and-whisker plot of the data sets can be different. To do so, let's consider two example data sets. Keep in mind that there are many possible examples.
Data Set1:
0, 1, 3, 4, 4, 5, 6, 6, 7, 8 ,9
Data Set2:
1,2,4,4,5,5,6,7,8,9,10
Let's find the five-number summary of each data set and draw its box-and-whisker plot.
Data Set 1
Let's take a look at the data values.
0, 1, 3, 4, 4, 5, 6, 6, 7, 8 ,9
From the data, we can see that the greatest value is 9 and the least value is 0. Additionally, the first quartile is 3, the third quartile is 7, and the median is 5.
We can now find the range of the data. Recall that the range is the difference between the greatest value and least value.
Range: 9- 0=9
We can also calculate the interquartile range (IQR). The IQR is the difference between the third quartile Q_3 and first quartile Q_1.
IQR: 7- 3=4
Now, let's draw the box-and-whisker plot of the data. We will start with a number line that includes the least and greatest values. Also, let's graph points above the number line for the five-number summary.
Finally, we can draw a box using Q_1 and Q_3. Then draw a line through the median and the whiskers from the box to the least and greatest values.
Data Set 2
Again, let's take a look the data.
1,2,4,4,5,5,6,7,8,9,10
In this case, the greatest value is 10 and the least value is 1. Additionally, the first quartile is 4, the third quartile is 8, and the median is 5.
Now, let's find the range and interquartile range of the data.
Range:& 10- 1=9
IQR:& 8- 4=4
In the same way as before, we can draw a box plot for the data set.
Conclusion
Now, let's take a look at the box-and-whisker plots.
We have found two data sets that have the same median, range, and interquartile range. However, we can see that their box-and-whisker plots are not equal. Therefore, if two data sets have these key pieces of information in common, the box-and-whisker plots can still be different.
